So, I have been working on this problem for a while and cannot figure out how to do it...so I have come here for help. Here it is...A cylinder with a diameter of 10 inches is hoisted by a chain on a hook (the chain is wrapped around the cylinder and leaves it and comes to a point at the hook...I have attatched a picture, not drawn to scale...) the chain is 38 inches long, what is the height of the space between the top of the circle and the point of the chain?I do not just want the answer, I would also like to know how you got the answer if possible (with steps) so I can see how close I was to it.
Basically, you need the angle that the unshaded(black) sector makes to find the height of the space between the top of the circle and the point of the chain. I will show you what I mean. First, you need to realize that the two parts of the chain that are going off the cylinder and towards each other and finally intersecting, are actually tangent to the cylinder(Makes a right angle with the cylinder). Therefore, if you let the angle that the unshaded sector makes be θ and let the height of the space between the top of the circle and the point of the chain be h, then you get that the total length of the chain equals: 10π(1 - θ/360) + 2√((h + 5)^2 - 5^2) = 38 inches 10π(1 - θ/360) + 2√(h^2 + 10h) = 38 inches Now you can clearly see that you need that angle to solve for h.
